Scientific.Functions.Rational.RationalFunction

Package Scientific :: Package Functions :: Module Rational :: Class RationalFunction |
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# Class RationalFunction

Rational Function

Instances of this class represent rational functions in a single variable. They can be evaluated like functions.

Rational functions support addition, subtraction, multiplication, and division.

Instance Methods
__add__(self, other) |
__call__(self, value) |
__coerce__(self, other) |
__div__(self, other) |
__init__(self, numerator, denominator=`[`1.0`]`) |
__mul__(self, other) |
__radd__(self, other) |
__rdiv__(self, other) |
__repr__(self) |
__rmul__(self, other) |
__rsub__(self, other) |
__sub__(self, other) |
(Scientific.Functions.Polynomial.Polynomial, RationalFunction) |
divide(self, shift=0) Returns: a polynomial and a rational function such that the sum of the two is equal to the original rational function. |
`Numeric.array` |
poles(self) Find the poles (zeros of the denominator) by diagonalization of the associated Frobenius matrix. |
`Numeric.array` |
zeros(self) Find the zeros (roots) of the numerator by diagonalization of the associated Frobenius matrix. |

Class Variables
| is_rational_function = `1`

Method Details

### __init__(self, numerator, denominator=`[`1.0`]`) (Constructor) |
Parameters: `numerator` (Scientific.Functions.Polynomial.Polynomial or `list` of numbers) - polynomial in one variable, or a list of polynomial coefficients `denominator` (Scientific.Functions.Polynomial.Polynomial or `list` of numbers) - polynomial in one variable, or a list of polynomial coefficients

### divide(self, shift=0) |
Parameters: `shift` (`int` (non-negative)) - the power of the independent variable by which the numerator is multiplied prior to division Returns: (Scientific.Functions.Polynomial.Polynomial, RationalFunction) a polynomial and a rational function such that the sum of the two is equal to the original rational function. The returned rational function's numerator is of lower order than its denominator.

### poles(self) |
Find the poles (zeros of the denominator) by diagonalization of the associated Frobenius matrix. Returns: `Numeric.array` an array containing the poles

### zeros(self) |
Find the zeros (roots) of the numerator by diagonalization of the associated Frobenius matrix. Returns: `Numeric.array` an array containing the zeros